To determine how many gallons of fuel a motorcycle will need to travel 60 kilometers, we need to follow a few logical steps:
1. Convert kilometers to miles:
Since we know that [tex]\(1 \text{ mile} = 1.6 \text{ km}\)[/tex], we start by converting the given distance in kilometers to miles.
The distance to be traveled is 60 kilometers. Using the conversion factor:
[tex]\[
\text{Distance in miles} = \frac{\text{Distance in kilometers}}{\text{Conversion factor}}
\][/tex]
[tex]\[
\text{Distance in miles} = \frac{60 \text{ km}}{1.6}
\][/tex]
2. Performing the division:
[tex]\[
\text{Distance in miles} = 37.5 \text{ miles}
\][/tex]
3. Calculate the gallons of fuel needed:
The motorcycle can travel 70 miles for each gallon of fuel. To find out how many gallons it will need to travel 37.5 miles, we can use the formula:
[tex]\[
\text{Gallons needed} = \frac{\text{Distance in miles}}{\text{Miles per gallon}}
\][/tex]
[tex]\[
\text{Gallons needed} = \frac{37.5 \text{ miles}}{70 \text{ miles/gallon}}
\][/tex]
4. Performing the division:
[tex]\[
\text{Gallons needed} \approx 0.5357 \text{ gallons}
\][/tex]
Given the options:
a. 0.2
b. 0.5
c. 0.8
d. 1.4
The answer closest to 0.5357 gallons is option b.
Therefore, the motorcycle will need approximately [tex]\(0.5\)[/tex] gallons of fuel to travel [tex]\(60\)[/tex] kilometers.
